Question

Felipe is solving this system of equations. He got (4, 7) as his solution.1.5x+2y=202.5x−5y=−251.5x+2y=202.5x−5y=−25Is Felipe correct?No, because the solution does not check for both equations.No, because the solution does not check for both equations.

Answer 1

Given the next system of equations:

$\begin{gathered} 1.5x+2y=20\text{ (eq. 1)} \\ 2.5x-5y=-25\text{ (eq. 2)} \end{gathered}$

To check if (4, 7) is a solution to the system of equations, we have to substitute this point into the equations and verify if they are satisfied.

Point (4, 7) means that x = 4 and y = 7. Substituting these values into equation 1, we get:

$\begin{gathered} 1.5\cdot4+2\cdot7=20 \\ 6+14=20 \\ 20=20\text{ (True)} \end{gathered}$

Substituting x = 4 and y = 7, into equation 2, we get:

$\begin{gathered} 2.5\cdot4-5\cdot7=-25 \\ 10-35=-25 \\ -25=-25\text{ (True)} \end{gathered}$

Felipe is correct because the solution checks for both equations